Tsukehiki, White extends into the centre
The intention of is (quite obviously) to build influence toward the center. White is however granting Black quite a large corner territory.
The joseki continues with through
(it is very unlikely that Black will play tenuki instead of cutting;
at
is a fighting move only available when White is already strong to the right).
Black takes the corner territory, White gets influence towards the top and the center. Clearly the cutting point at a makes an important ladder relationship, now.
White presumably thought about this ladder before choosing this variation, with in the first diagram: making this a ladder strategy.
instead of
from the previous diagram might seem better, taking sente, but if Black actually does play tenuki,
through
gouges out Black's corner.
Taking away the corner territory (and even the eyespace) is larger than a black move elsewhere would be. (See though tenuki is always an option.)
-- AndreEngels